A usability test was conducted to evaluate the design of a store website. The times to complete a certain task were recorded for a sample of 48 users. The sample mean time was 70 seconds with a 95% margin of error of 10 seconds. In other words, researchers estimated with 95% confidence that the mean time to complete the task was between 60 and 80 seconds for all website users. Only one of the following statements is true. Select the correct statement. 1. the probability that the mean time μ will fall between 60 and 80 is 0.95.
2. If many samples are collected from the same population, about 95% of the samples will produce confidence intervals that contain the population mean μ.
3. If a second sample from the same population is selected and a 95% confidence interval is constructed, the new confidence interval will be the same as the 95% C. I. defined in the first study.
4. If the study is repeated, and a new 95% confidence interval is computed, there is 95% chance that the new interval contains the sample mean value >= 40 seconds.

2. If many samples are collected from the same population, about 95% of the samples will produce confidence intervals that contain the population mean μ.

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

So the correct option is given by:

Option 2, as we will be 95% sure that the population mean will be in the interval, which can be interpreted that from many samples, about 95% will contain the population mean.

step-by-step explanation:

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)